F(x)=-x^2-4x+8

Solution for F(x)=-x^2-4x+8 equation:

(F)=-F^2-4F+8

We move all terms to the left:

(F)-(-F^2-4F+8)=0

We get rid of parentheses

F^2+4F+F-8=0

We add all the numbers together, and all the variables

F^2+5F-8=0

a = 1; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·1·(-8)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{57}}{2*1}=\frac{-5-\sqrt{57}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{57}}{2*1}=\frac{-5+\sqrt{57}}{2}
$